Which expression can be used for the missing side length of the rectangle?

A rectangle with a width of 2x inches and a diagonal length of 8x inches is given. The length of the rectangle is marked as ? inches.

A. x√6
B. 2x
C. x√30
D. 2x√15

Length = 2x✓15

Step-by-step explanation:

A rectangle has a width of 2x inches and a diagonal length of 8x inches. We are told to find the length of the rectangle. The square of the diagonal is the addition of the square of the length and square of the width.

Adjacent² = length² + width²

(8x)² = length² + (2x²)

Length² = 64x² - 4x²

Length² = 60x²

Length = ✓60x²

Length = ✓4 × ✓15 × ✓x²

Length = 2 × ✓15 × x

Length = 2x✓15